Quickstep- "surely the teacher doesn't call out the open telemark as 3-4,1,2..."

Of course he/she does!

The simple fact is that it depends on what level student we are teaching. At the lowest beginner level, we avoid figures and timing which might confuse the uninitiated, but at a slightly higher level, introducing the notion that the "slow" is often danced on the 3-4 is a must. As you should be made aware, both the Natural turn and Change of Direction are danced with three slows and are often followed by a feather step. The technique book is correct on this point and it is obvious that the following feather is danced "slow" on 3-4, as soon as a student can handle that. As a practical matter, teachers often add an extra "slow" to the Natural Turn so that the beginner-beginner can continue on the same timing.

But it isn't just "3-slow" figures. When teaching a silver level student, the Natural Telemark is a key, and most useful, figure, -and it is danced S,Q,Q,Q,Q, which also results in the following figure's LF "slow" being on 3-4. After the "magic 30" is mastered by my Bronze Student, I would replace the Natural Turn/Impetus/Reverse Turn with a Natural Telemark followed by an Open Telemark and Feather Ending. This would then be followed with the three step,- and all of this would be danced with the "slow" on 3-4. Replacing the three step with a COD or following the three step with another Natural Turn or Natural Telemark returns the student to familiar territory.

You need to stop watching, (or at least trying to emulate), high level pros. They often break the "rules" to good effect. John Wood would often commence his Foxtrot with a Change of Direction started on 3-4 (DW) to give the competitors he was about to defeat a head start. Then he would dance a simple sequence on conventional time for maybe 5 bars- just to show he could do that. He would then dance an impetus turn and end with a feather finish danced with a slow as the (RF) last step and proceed to dance his next sequence QQS - 2,3,4-1 - yes - as in Rumba. Every judge knew it was "off-time" but he (and his all-time great partner Ann Lewis) made it beautiful, and the judges made him world champion.

*You* can't do that. And neither can I.

Get yourself a qualified ISTD teacher. And if your teacher ever tells you you can't dance a "slow" in Foxtrot on 3-4, GET ANOTHER TEACHER !!